10/07 Compound Interest Practice

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What is compound interest?

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Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

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How is compound interest different from simple interest?

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Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods, while simple interest is calculated only on the principal amount.

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What does the variable 'P' represent in the compound interest formula?

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In the compound interest formula, 'P' represents the principal amount, which is the initial sum of money invested or borrowed.

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What is the formula for calculating compound interest?

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The formula for calculating compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

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What does 'n' represent in the compound interest formula?

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In the compound interest formula, 'n' represents the number of times that interest is compounded per year.

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How do you calculate the future value of an investment compounded monthly?

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To calculate the future value of an investment compounded monthly, use the formula A = P(1 + r/12)^(12t), where r is the annual interest rate and t is the number of years.

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What is continuous compounding?

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Continuous compounding refers to the process of calculating interest on an investment or loan at every possible moment, leading to the formula A = Pe^(rt), where e is Euler's number (approximately 2.71828).

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How do you determine the total amount paid on a loan with compound interest?

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To determine the total amount paid on a loan with compound interest, calculate the future value using the compound interest formula and then subtract the principal amount.

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What is the effect of a higher interest rate on compound interest?

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A higher interest rate increases the amount of interest earned or paid over time, leading to a larger future value of the investment or loan.

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How does the frequency of compounding affect the total interest earned?

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The more frequently interest is compounded, the more interest will be earned, as interest is calculated on previously accumulated interest.